Q.Out of NaCl and AgCl, which one shows Frenkel defect and why?

Concept: Frenkel defect – a lattice imperfection where a smaller cation leaves its normal site and occupies an interstitial position, creating a vacancy-interstitial pair.

For a Frenkel defect to form, two conditions must be met:

1. Large size difference between cation and anion – the cation must be small enough to fit into interstitial voids while the anion remains large.

2. Low coordination number – smaller cations can more easily squeeze into interstitial sites.

In NaCl: $r_{\text{Na}^+} = 102 \text{ pm}$ and $r_{\text{Cl}^-} = 181 \text{ pm}$. The size difference is moderate, and Na⁺ is not small enough to comfortably occupy interstitial sites. NaCl predominantly shows Schottky defect (cation-anion pair vacancies).

In AgCl: $r_{\text{Ag}^+} = 126 \text{ pm}$ and $r_{\text{Cl}^-} = 181 \text{ pm}$. Although Ag⁺ is larger than Na⁺, it has high polarizability and can distort to fit into interstitial voids. The key is that Ag⁺ has a pseudo-noble gas configuration (4d¹⁰) making it more polarizable and mobile.

Why size matters for Frenkel defects

A Frenkel defect occurs when an ion leaves its regular lattice position and squeezes into an interstitial site (a gap between the normal lattice positions). The original site becomes vacant, but the ion hasn't left the crystal—it's just relocated to a cramped spot it doesn't normally occupy.

For this to happen, the displaced ion must be small enough to fit into these tight interstitial spaces without causing catastrophic strain in the crystal. This is why Frenkel defects are almost always associated with the smaller ion in an ionic compound, and only when there's a substantial size mismatch between cation and anion.

Comparing NaCl and AgCl

Let's look at the ionic radii:

Notice that Ag⁺ is actually larger than Na⁺! So why does AgCl show Frenkel defects while NaCl doesn't?

The key lies not in absolute size but in polarizability and effective size in the lattice.

1. Silver's electron configuration: Ag⁺ has the configuration [Kr]4d¹⁰. Those ten d-electrons form a diffuse, easily polarizable cloud. When Ag⁺ approaches an interstitial site, this electron cloud can deform and compress, allowing the ion to effectively "squeeze" into spaces that its nominal ionic radius would suggest are too small.

2. Sodium's electron configuration: Na⁺ has [Ne], a compact noble-gas core. This is a rigid, spherical electron distribution that resists deformation. Na⁺ behaves like a hard sphere—it cannot compress to fit into interstitial sites in the NaCl lattice.

3. The size ratio: In NaCl, the ratio $r_{\text{Na}^+}/r_{\text{Cl}^-} \approx 0.56$, which is close to the ideal for octahedral coordination. The cation fits snugly in its octahedral hole with little room to spare, and interstitial sites are far too small. In AgCl, despite Ag⁺ being nominally larger, its polarizability makes it behave as if it were smaller and more "slippery."

4. Lattice structure: Both adopt the rock-salt (NaCl) structure, but the polarizable nature of Ag⁺ combined with the larger, more polarizable Cl⁻ creates a softer lattice where ionic displacement is energetically feasible.

Why NaCl prefers Schottky defects

In NaCl, both ions are relatively similar in size and both are hard spheres. When defects form, it's energetically favorable for a pair of ions (one Na⁺ and one Cl⁻) to leave the lattice entirely, maintaining charge neutrality. This is a Schottky defect—vacancies without interstitial occupation.